On occasion we at runPCrun have had first-time customers come to us that haven't backed up their data and have had their hard drives die on them, leaving them with their data inaccessible.
When software recovery ceases to be an option or the risk too high we recommend it get sent to Disklabs* clean rooms for recovery and so they've saved our customers many times.
Good value for money, quick, operate a "no fix, no fee" service and have excellent customer service to boot. Avoid companies that will charge you £70/100 just for diagnostics, regardless of whether or not they can actually recover your data.
* means there is some referral or partnership with these suppliers via the links given. Check out our stance on reviews and recommendations